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 A302689 a(n) = 4 + 2^n - 4*n. 0
 2, 0, 0, 4, 16, 44, 104, 228, 480, 988, 2008, 4052, 8144, 16332, 32712, 65476, 131008, 262076, 524216, 1048500, 2097072, 4194220, 8388520, 16777124, 33554336, 67108764, 134217624, 268435348, 536870800, 1073741708, 2147483528, 4294967172, 8589934464 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the number of connected dominating sets and total dominating sets in the n-path complement graph for n > 1. LINKS Eric Weisstein's World of Mathematics, Connected Dominating Set Eric Weisstein's World of Mathematics, Path Complement Graph Eric Weisstein's World of Mathematics, Total Dominating Set Index entries for linear recurrences with constant coefficients, signature (4,-5,2). FORMULA G.f.: -2*x*(1 - 4*x + 5*x^2)/((-1 + x)^2*(-1 + 2*x)). a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). a(n) = A258547(n-5) for n > 5 (conjectured). a(n) = 4 * A000295(n) for n > 1. - Alois P. Heinz, Apr 12 2018 MATHEMATICA Table[4 + 2^n - 4 n, {n, 20}] LinearRecurrence[{4, -5, 2}, {2, 0, 0}, 20] CoefficientList[Series[-(2 (1 - 4 x + 5 x^2)/((-1 + x)^2 (-1 + 2 x))), {x, 0, 20}], x] PROG (PARI) a(n) = 4+2^n-4*n; \\ Altug Alkan, Apr 12 2018 (MAGMA) [4+2^n-4*n : n in [1..45]]; // Vincenzo Librandi, Apr 13 2018 CROSSREFS Cf. A258547. Sequence in context: A048243 A159814 A169774 * A289088 A057611 A329959 Adjacent sequences:  A302686 A302687 A302688 * A302690 A302691 A302692 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Apr 11 2018 STATUS approved

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Last modified September 25 18:42 EDT 2020. Contains 337344 sequences. (Running on oeis4.)